Photon vs Energy Magnitude Systems and the Measurement of the Cosmological Parameters

The relative brightnesses of standard candles have long been known to be potentially powerful probes of distance. The distance modulus, the difference between observed and absolute magnitudes, has been associated with the values of the cosmological parameters: Hubble's constant H_0, the mass density Omega_M and the cosmological constant Omega_Lambda. In the literature the relationship between these parameters and the distance modulus is calculated for an energy magnitude system; the Johnson-Cousins magnitude system used in observations is in fact a photon-counting system. In this paper, we present the relation between observed and absolute photon magnitudes in terms of the familiar energy distance modulus and derive the correct form of the K-correction. The differences between energy and photon systems are small relative to the measurement errors of contemporary high-redshift supernova searches. The distinction must be made, however, for precision cosmological measurements such as those planned for Type Ia supernovae.